Abstract
Background: Modeling with the complex random phenomena that are frequently observed in reliability engineering, hydrology, ecology, medical science, and agricultural sciences was once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. To address these issues, scientists have previously discussed a variety of bounded and unbounded, simple to complex lifetime models. Methods: We discussed a modified Lehmann type II (ML-II) model as a better approach to modeling bathtub-shaped and asymmetric random phenomena. A number of complementary mathematical and reliability measures were developed and discussed. Furthermore, explicit expressions for the moments, quantile function, and order statistics were developed. Then, we discussed the various shapes of the density and reliability functions over various model parameter choices. The maximum likelihood estimation (MLE) method was used to estimate the unknown model parameters, and a simulation study was carried out to evaluate the MLEs' asymptotic behavior. Results: We demonstrated ML- II's dominance over well-known competitors by modeling anxiety in women and electronic data.
Highlights
Over the last two decades, researchers' increasing interest in the development of new models has explored the remarkable characteristics of the baseline model
Modified Lehmann type II model We developed a potentiated lifetime model known as the modified Lehmann type II (ML-II) model
Application we explore the application of ML-II in medical science and engineering data
Summary
Over the last two decades, researchers' increasing interest in the development of new models has explored the remarkable characteristics of the baseline model. Arshad et al.[4,5] developed bathtub-shaped failure rate and PF models followed by L–II and L–I families, respectively, and explored their applications in engineering data. The ML-II is said to follow a random variable X if its associated CDF and corresponding probability density function (PDF) are given by FMLÀIIðx; α, βÞ. Limiting behavior Propositions 1 and 2 discuss the limiting behavior of the ML-II's cumulative distribution (CDF), density (PDF), reliability (S(x)), and failure rate (h(x)) functions for x ! The residual life function of random variable X, RðtÞ 1⁄4 ðX À t=X > tÞ, is the likelihood that a component whose life says x, survives in the different time intervals at t ≥ 0 It can be written as follows: SRðtÞÀMLÀII ðx; Sðx þ SðtÞ tÞ. Parameter/ variable range α,β > 0, 0
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